Problem: Solve the equation. $\dfrac5{13}=t-\dfrac{6}{13}$ $t=$
Explanation: Let's add to get $t$ by itself. $\begin{aligned}\dfrac5{13}&=t-\dfrac{6}{13}\\ \\ \dfrac5{13} {+\dfrac6{13}}&= t-\dfrac6{13}{+\dfrac6{13}}~~~~~~~~~~~~{\text{add }\dfrac6{13}} \text{ to each side to get } t \text{ by itself }\\ \\ \dfrac5{13} {+\dfrac6{13}}&= t-\cancel{\dfrac6{13}}{+}\cancel{{\dfrac6{13}}} \\\\ \dfrac5{13} {+\dfrac6{13}}&= t\end{aligned}$ The answer: $t={\dfrac{11}{13}}$ Let's check to make sure. $\begin{aligned} \dfrac5{13}&=t-\dfrac{6}{13}\\\\ \dfrac5{13}&\stackrel{?}{=} {\dfrac{11}{13}}-\dfrac6{13} \\\\ \dfrac5{13} &= \dfrac5{13} ~~~~~~~~~~~~~~~~\text{Yes!} \end{aligned}$